[t]
\(\mathcal {F}=\lbrace F_1, \dots , F_M\rbrace \) , \(u^-_{\mathbf {\omega }}\) 
Common class mean direction \({\mathbf {\theta }}\) 
\({\mathbf {\theta }}\leftarrow \rm {norm}(\sum _{i=1}^M F_{i1})\) *Initialization
(*[f]Iterations)\(t \leftarrow 1\)  to T
(*[f]E-step)\(i \leftarrow 1\)  to M
\(\mathbf {o}_{ij} \leftarrow \kappa {\mathbf {\theta }}^\top F_{ij} - \log u_{{\mathbf {\omega }}}^-(F_{ij})~~~\forall j\in [1, P]\) 
\(\mathbf {w}_i \leftarrow \text{softmax}(\mathbf {o}_i)\) *Update Soft labels

\({\mathbf {\theta }}\leftarrow \rm {norm}(\sum _{i=1}^M \mathbf {w}_i^\top F_i)\) 
*M-step

Common Object Localization

We remark that our initial direction is similar to what is used as class
mean in prototypical networks [1]}. What makes us
different is EM steps that refine the estimated mean by focusing on the common
objects and discarding background parts of the image.
